On 25 Dec 2012, at 04:10, Stephen P. King wrote:

On 12/24/2012 7:27 PM, meekerdb wrote:
On 12/24/2012 3:43 PM, Stephen P. King wrote:

On 12/24/2012 3:22 PM, meekerdb wrote:
On 12/24/2012 11:41 AM, Stephen P. King wrote:

Dear Roger,

Flies can unify their vision because the distance between their individual eyes is small and the number is finite. One can still manage to get a mutually commuting set of observations in these conditions. When one has an arbitrarily large distance between a pair of "eyes" and the number of them is infinite then it is impossible to have a mutually commuting set of observations. This is the problem of omniscience.

I have two eyes and no problem unifying them. Vision takes place in the brain, not the eyes.

Hi Brent,

    I think you missed the point I was trying to make.

Apparently. You are basing this impossibility on a literal infinity - not just "very very many"? In that case I'd agree because the literal infinity is itself impossible.

Pfft, really? Oh my, you are hard up to save an obviously false idea! If the infinity is merely potential, the situation is worse! Think about it, how many different 1p are *possible*? Many, at least! I submit to you that the number must be infinite. This would be equivalent to an infinite number of propositions.

The number of human 1p is infinite if you let the human skull growing arbitrarily.

It should be obvious that to find a SAT solution to such is impossible for any classical system.

SAT is Sigma_0. SAT is decidable. We can find all the SAT solutions, if patient enough. No doubt that it can take some time to see if a classical propositional formula with 10^1000 propositional variables is a tautology. P = NP would not necessarily help, because the polynomial bounding complexity can be quite growing if it has big coefficient.

For biology and theology the interesting things happens on the border of the Sigma_1 complete structures. Only bankers and engineers really need to talk the Sigma_0, and subtractability issues. By comp, we will have to derive why, from the geometry and topology of the border of the Sigma_1, seen in 1p. UDA and AUDA illustrates that the border get his geometry and topology from self-reference, starting from sigma_1 sentences (which represent in arithmetic the UD states).



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